08. THE RULE OF PARALLELOGRAM FOR ELEMENTARY PARTICLES AND FOR DIFFERENT TYPES OF FORCES

08. THE RULE OF PARALLELOGRAM FOR ELEMENTARY PARTICLES AND FOR DIFFERENT TYPES OF FORCES

The world around us is woven from Forces, as Force - is Ether and Ether in the universe is everywhere. Force - this is what tends to move something from the place.

One of the differences between mechanics of bodies and mechanics of stable elementary particles is that the particles under the influence of forces may only move.

They can not to be deformed and disintegrate for one reason - they are inseparable. While a body (or even unstable particle - conglomerate), when a force acts on it (or forces), may move and be deformed and broken down.

In mechanics of bodies (in classical mechanics) there is a wonderful way to help find out in which direction the body will tend to move under an influence of all forces that act on it. Also, to calculate the resultant forces. This method is well known as the Rule of the Parallelogram of Forces.

It was opened by Galileo Galilei, and the precise definition of this rule was given by Pierre Varinon in 1687.

The Rule of Parallelogram of Forces says that the resultant force vector is the diagonal of the parallelogram formed by the vectors of two summands of forces as on the sides.

This rule surprisingly well helps to calculate precisely the direction in which a body will move (or will try to move) if it is acted upon more than one of the Force. And in our world every body is always at the same time experiencing an impact of the myriad of external forces (because any particle in any chemical element - is a source of Force).

Moreover this Rule is perfectly suited for elementary particles. With it, we can see the direction in which an elementary particle will shift at every moment of time if two or more Forces act on it at the same time. And also we can know the ratio of the values ​​of Forces - an original and a resultant. And the type of each of the forces can be any. The diagonal of Parallelogram - this is an indication of direction, as well as a measure of the resultant Force. However, please note an important factor - a new Parallelogram of Forces should be built to each next moment of being of the particle.

Let's take a little closer look at the essence of the Rule of Parallelogram. And in the course of this analysis we will give it a slightly different name – the Rule of Subordination to the Dominant Force. This will allow us to better understand the characteristics of behaviour of elementary particles (and any conglomerates of particles) because the Rule of Parallelogram in the form of which it exists now, not fully reveal the meaning of what is happening with the particle when more than one Force affects on it. For example, it says nothing about the fact that there are different types of Forces.

The Dominant Force – is the Force which is greater in magnitude. As we said earlier, a magnitude of a Force - is the rate of ethereal flow entraining the particle. Moreover, Ether just fills a particle can act as an ethereal flow (as in the case of the Force of Pressure of the particle surface).

The Rule of Subordination to the Dominant Force (the Rule of Parallelogram) represents that the particle, on which act more than one Force, to the greatest extent will be subject to the higher of them. What does this mean? This means that the vector of resultant forces at each moment will be more biased towards the vector of Force with the highest magnitude. That is, the biggest Force prevails, but other Forces also have an effect on the position of the resultant force vector. You can further specify the name of the rule - Subordination to the Dominant Force with an accounting of actions of the remaining forces.

The Dominant Force shifts the vector of resultant Force in its own direction more than others. And other, smaller forces do not give this vector to fully submit to this biggest Force. They pull the vector in their direction in proportion to their magnitude.

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In general, in the analysis of any situation in which an elementary particle is influenced by more than one force it is necessary to consider a number of factors. First, you need to know how many forces acting on the particle and the value of each of them. Secondly, you need to know at what angle the vectors of Forces are placed one against the other. And third, you must consider the type each of forces. Only evaluating all these factors, we can try to calculate the direction and velocity of a particle at every moment of time. Let's take a little closer look at these factors.

1) A value and total quantity of forces acting on a particle must be assessed in each particular case.

In that case, if a number of forces acting on the particle is greater than two, we should do the same as in the case of bodies. We need to build the parallelogram for two forces. Then we will make the next parallelogram, using the resulting vector and the next of forces. And so on, until it will be account all of Forces.

2) An angle between the vectors of forces acting on a particle is very important in clarifying the magnitude and direction of the resultant force.

A) An angle between vectors of Forces is from 0˚ to 90˚.

In this case there is some kind of summation of the Forces acting on the particle. Of course, the resultant Force will not be exactly equal to the sum of two Forces acting on the particle. But in any case it will be more than either of two forces, on whose vectors we build the parallelogram. You can see this in the value of the diagonal of a parallelogram. And the sharper an angle is, the bigger the value of the resultant Force is.

An extreme case of an acute angle is 0˚, i.e. absence of corner. Force vectors are on one line, and their direction is the same. In this case, it is impossible to construct the parallelogram. Instead of it - straight, we put on it two segments, each of which is equal to one of the operating Forces. At 0˚ is the total summing of Force vectors.

B) An angle between vectors of Forces is more than 90˚.

In this case you can see from the picture, there is a kind of subtraction Forces. The resultant Force is always more than the smaller of two Forces and less of the biggest one. Confirmation of this is a value of the diagonal. And the greater an angle is, the smaller the resultant force is.

An extreme case of an obtuse angle is an angle of 180˚. Force vectors are collinear. However, unlike an angle equal to 0˚, the vectors are in opposite directions. In this extreme case, there is just subtraction from the vector of greater force the vector of less. The difference is exactly corresponds to the magnitude of the resultant force.

In any case, for any value of an angle, the vector of resultant Force is always largely shifted to the larger of two Forces. That is, the biggest Force makes the particle to shift in its own direction more than other.

3) Finally, we present information about how the Rule of Parallelogram depends on the type of Forces acting on a particle.

A) Even though sources of all types of forces are different, and their effect on a particle can be compared, since each of the forces tends to cause the particles to move. And so, even if the forces acting on a particle are of different types, you can build the Parallelogram of Forces on the vectors, and its diagonal will be showing the direction in which the particle will move.

The value of the Force vector is greater, the greater a force is. A Force is greater, the greater is the velocity with which the particle shifted in this direction if another Force would not act on it (or other Forces).

The length of the vector of resultant Force – of the diagonal - corresponds to the rate at which a particle will be displaced by the action of two Forces applied to it.

B) We have established earlier that there are only four main types of forces. When Galileo deduced the Rule of Parallelogram, it is obvious that he has done in relation to the Forces, with which some bodies put pressure on others or drag them, making to move. This type of Force is called in this book the Force of Pressure of the Particle Surface. We have heard a little about that the Rule of Parallelogram is used for Gravity Force. Especially, this limit applies to Repulsive Force and Force of Inertia, the first of which is almost not recognized by science, and the second is not known at all.

But anyway, this rule is universal and can be used for any of four types of forces - Pressure of the Particle Surface, Attraction, Repulsion and Inertia. However unchanged it can be applied only to Force of Pressure of the Particle Surface, i.e. for the same event, which is described by Galileo for bodies.

Two bodies affect on the body from both sides - or put pressure on it or drag. In our case, two particles press on the particle (they can’t mechanically drag the particle).

Taken separately a free particle will never cause long-term pressure on other particle, if only the Force of Attraction doesn’t act on it from another particle. Alternatively, if particles are included into bodies and they squeeze each other and any particle between them. Therefore, in our case it is one-stage pressure on the particle of two particles as a result of the collision with it. When two particles collide with a particle, it starts to move by inertia, exactly in accordance with the Rule of Parallelogram. The diagonal (resultant Force vector) shows the direction in which the particle will move. How long inertial motion will, depends on the rate at which the particles were moving at the time of the collision with it, on the angle between the vectors of Forces and more on the quality of the particle itself.

C) The only difficulty that we face in the construction of Parallelogram of Forces is related to Attraction and Repulsion Forces. Here it is spoken even more likely not about the difficulty but about of strangeness. Sources of forces of attraction or repulsion are located from the particle on one or another distance. However, the particle feels effect of these forces directly. This is not surprising, because a gravitational interaction or anti-gravitational propagates instantaneously. This instantaneous dissemination is explained by the fact that an ethereal "cloth" – it is a kind of monolith that fills homogeneously the entire universe. And the appearance in this cloth of any excess or deficiency of Ether is immediately felt at any distance.

In this case, when types of Forces acting on a particle, are different, the vector of Forces must indicate the direction in which the Force strives to displace the particle. For example, if a Force of Attraction acts on a particle, so the vector will be directed to an object, the source of this force, and not of it. But in the case of Repulsion Force all is the opposite. The vector will be directed from the source of the Force.

As the Force of Pressure of the Particle Surface, everything is the same as in mechanics of bodies. In this case, the source of Force is in direct contact with the particle - collides with it. And vector of this Force is directed in the same direction as the motion vector of a particle whose surface exerts pressure.

And finally, there is last of Forces – Force of Inertia. The presence of this force can be discussed only in the case if a particle is moving by inertia. If the particle is not moving by inertia, there is no Force of Inertia. A vector of Inertia Force always coincides with the vector of motion of particle at this moment. A vector of Inertia Force is Ether emitted by the rear Hemisphere of particle.

D) Never happens that two forces acting on a particle were inertial, as a particle can move by inertia at each moment of time only in one direction.

E) If one or both of Forces acting on a particle relate to the type or of Attraction or Repulsion, the particle will move in parabola, gradually displacing by the action of the larger Force.

If one of Forces acting on a particle refers to the type of Attraction or Repulsion, and the second - is Force of Inertia, while the trajectory of the particle is also parabolic.

F) It is never at the same time Forces of Attraction and Repulsion act on a particle, and their vectors would on the same line and would be opposite directions. The reason is that Force of Attraction and Force of Repulsion are Forces-antipodes. A vector of Force of Attraction is directed to the source of Force. And a vector of Repulsion Force is directed from it. Therefore, if sources of Attraction and Repulsion Forces are located on opposite sides of a particle, the vectors of their forces will be summed.

If sources of Forces are on one side of a particle, the particle will feel only any one of Forces - either of Attraction or Repulsion. And all because the Fields of Attraction and Repulsion screen and affect on the value of each other.

But in any case, the Rule of Parallelogram can be used to any particle, to determine with its help a direction and magnitude of resultant Force. In accordance with the magnitude and direction of the vector a particle will be displaced in a given moment of time.

All that we have just been said of the Rule of Parallelogram for particles can be fully used for bodies.